Production and allocation policies in a two-class inventory system with time and quantity dependent waiting costs

This paper presents an integrated production and inventory allocation model in a two-echelon supply chain system. The higher echelon is a manufacturer, who produces a single commodity. The lower echelon consists of two types of major commodity distributors who might face stochastic or deterministic demands from multiple retailers. Our analytical model provides optimal decision policies that minimize total production and customer waiting costs from the manufacturer's perspective when there are time and quantity dependent customer waiting costs. We identify the value of the integrated policy and compare it with typical approximations such as aggregating the multiple demands or applying the single demand multiple times.